There used to be a great project that brought all the London public library catalogues together
“WILL – “What’s in London’s Libraries” has just been launched. This is a new service for users and librarians of London libraries. It will bring together all 33 London library catalogues into a single, searchable database. It also includes a variety of information such as activities programmes and special collections. The URL is: http://www.londonlibraries.org.uk/will”
Sadly long defunct
Increasing numbers of local authorities are in the same catalogue as part of a consortium so you can search collections for a bug chunk of people there (London plus Essex) https://llc.ent.sirsidynix.net.uk/client/en_GB/default
The BL have been working on a proposal for a single national platform for public libraries for longer than I care to think about. It won’t integrate the search anyway I don’t think.
There may well be other decent options but not my specialist corner of library land!